Problem 60 - Chemistry The Central Science In Si Units

Question

(a) If an electric car is capable of going \(225 \mathrm{~km}\) on a single charge, how many charges will it need to travel from Seattle, Washington, to San Diego, California, a distance of \(1257 \mathrm{mi}\), assuming that the trip begins with a full charge? (b) If a migrating loon flies at an average speed of \(14 \mathrm{~m} / \mathrm{s}\), what is its average speed in \(\mathrm{mi} / \mathrm{hr} ?\) (c) What is the engine piston displacement in liters of an engine whose displacement is listed as 450 in. \(^{3} ?(\mathbf{d})\) InMarch 1989 , the Exxon Valdezranagroundand spilled 240,000 barrels of crude petroleum off the coast of Alaska. One barrel of petroleum is equal to 42 gal. How many liters of petroleum were spilled?

Step-by-Step Solution

Answer

(a) 9 charges; (b) 31.29 mi/hr; (c) 7.37 liters; (d) 38,063,088 liters.

Step 1: Convert Distance from Miles to Kilometers

First, we need to convert the distance from Seattle, Washington to San Diego, California from miles to kilometers. The conversion factor is 1 mile = 1.60934 kilometers. Therefore,\[ 1257 \text{ miles} \times 1.60934 \frac{\text{km}}{\text{mile}} = 2023.44 \text{ km}. \]

Step 2: Calculate Number of Charges Required

Knowing the total travel distance in kilometers and the car's range on a single charge, calculate the number of full charges required. Divide the total distance by the distance per charge: \[ \frac{2023.44 \text{ km}}{225 \text{ km per charge}} \approx 8.99. \] Since you cannot use a fraction of a charge, round up to the nearest whole number. Thus, the car needs 9 full charges.

Step 3: Convert Speed from Meters per Second to Miles per Hour

To convert the loon's speed from meters per second (m/s) to miles per hour (mi/hr), first convert meters to miles (1 mile = 1609.34 meters) and seconds to hours (1 hour = 3600 seconds).\[ 14 \frac{\text{m}}{\text{s}} \times \frac{1 \text{ mile}}{1609.34 \text{ m}} \times 3600 \frac{\text{ s}}{\text{ hr}} \approx 31.29 \text{ mi/hr}. \] Thus, the loon's average speed is 31.29 mi/hr.

Step 4: Convert Engine Displacement from Cubic Inches to Liters

One cubic inch is equivalent to 0.016387064 liters. Multiply the engine displacement in cubic inches by this conversion factor: \[ 450 \text{ in}^3 \times 0.016387064 \frac{\text{L}}{\text{in}^3} \approx 7.37 \text{ liters}. \] The engine's piston displacement is approximately 7.37 liters.

Step 5: Convert Petroleum Volume from Barrels to Liters

First, convert barrels to gallons. One barrel of petroleum is equal to 42 gallons. Then convert gallons to liters, knowing there are approximately 3.78541 liters per gallon.\[ 240,000 \text{ barrels} \times 42 \frac{\text{gal}}{\text{barrel}} \times 3.78541 \frac{\text{L}}{\text{gal}} \approx 38,063,088 \text{ liters}. \] Approximately 38,063,088 liters of petroleum were spilled.

Key Concepts

Electric Vehicle Range Calculation

Electric vehicles (EVs) provide an environmentally friendly solution for transportation. Yet, understanding how far they can travel on a single charge is crucial when planning long trips. To determine the number of charges needed for a trip, you need to know the vehicle's range and the total distance to be traveled.
First, convert the trip distance from miles to kilometers, as the EV's range is often given in kilometers. For example, a distance of 1257 miles is converted using the factor of 1 mile = 1.60934 km, resulting in 2023.44 kilometers.
Next, divide the total distance by the range per charge. For an EV with a 225 km range, dividing 2023.44 km by 225 km/charge gives approximately 8.99. Always round up, as fractions of a charge aren't possible, resulting in 9 full charges needed.
Understanding this ensures efficient planning, avoiding interruptions due to unexpected recharging stops.

Speed Conversion

Speed conversion helps compare speeds across different units. Here, we convert speed from meters per second (m/s) to miles per hour (mi/hr), a more familiar unit for many. The conversion involves two key steps: converting meters to miles and seconds to hours.
To switch from meters to miles, use the fact: 1 mile = 1609.34 meters. For time, 1 hour = 3600 seconds. For example, a speed of 14 m/s is converted as follows:

• Convert meters to miles: 14 m/s × (1 mile / 1609.34 m)
• Convert seconds to hours: Result × 3600 s/hr

This gives approximately 31.29 mi/hr. Understanding this conversion is essential when interpreting speeds between metric and imperial systems.

Volume Conversion

Converting volume between measurement systems is crucial in various contexts, such as engine capacity or liquid quantities. Common conversions involve cubic inches to liters or gallons to liters.
For engine displacement, knowing that 1 cubic inch is 0.016387064 liters is useful. Thus, an engine listed at 450 cubic inches converts to:

• 450 in³ × 0.016387064 L/in³ ≈ 7.37 liters

This gives the engine's piston displacement in liters. Similarly, when converting between barrels and liters for liquid volumes, know 1 barrel equals 42 gallons, and there are 3.78541 liters per gallon. For example, 240,000 barrels is converted to liters by calculating total gallons first, then converting to liters.
This skill sets the foundation for understanding capacities in international standards.

Environmental Impact Calculation

Environmental impact assessments consider the quantities of materials, such as oil spills, in standard units like liters. Operation specifics, like the Exxon Valdez oil spill of 1989, demonstrate this need.
First, convert barrels to gallons using the relation 1 barrel = 42 gallons. For 240,000 barrels, this gives 10,080,000 gallons. Next, convert gallons to liters using the factor 1 gallon ≈ 3.78541 liters:

• 10,080,000 gallons × 3.78541 L/gallon ≈ 38,063,088 liters

Using liters, a widely accepted unit, helps in communicating and managing environmental data. This process demonstrates the importance of reliable conversions in assessing and mitigating environmental impacts accurately.